In this model, the lightest of the extra neutral particles: \(H^0\) , \(A^0\) , and \(D^0_{1,2,3}\)  could be a DM candidate, whose stability is guaranteed by the imposed \(Z_2\)  symmetry. In the following, we will focus on the case that DM is constituted solely by \(H^0\)  with a small charged scalar mixing \(s_\theta \) , in which our DM would be very similar to that in the well-studied inert doublet model [1]}, [2]}, [3]}. Furthermore, we concentrate on the low DM mass region with \(50 ~{\rm GeV} \leqslant M_{H} \leqslant 80~{\rm GeV}\)  [2]}, [3]}, in which a large \(H^0\) -\(A^0\)  mass splitting can be allowed for the generation of the right two-loop neutrino masses. In addition, the mass of \(S_2^\pm \)  should be higher than 90 GeV in order to escape the LEP bounds [6]}, so that the co-annihilation channels, such as \(H^0\) -\(A^0\)  and \(H^0\) -\(S_2^\pm \) , would be strongly suppressed and thus ignored.
